The effect of multiple representations-based and problem-based instruction in linear algebra on pre-service teachers' dimensions of understanding and self-efficacy perceptions

Abstract

The primary aim of this quasi-experimental study is to investigate whether teaching approaches that employ multiple representations-based (MRBI) and problem-based (PBI) instruction are more effective than traditional formalism-based instruction (FBI) in improving the performance and self-efficacy perceptions of pre-service elementary mathematics teachers (PEMTs) in a linear algebra course. Additionally, the study aims to explore the understanding of linear dependence/independence (LDI) and span concepts among three groups. Two of them received experimental instruction through MRBI and PBI approaches, and one was a control group that received FBI. The study group consisted of 90 PEMTs pursuing a bachelor’s degree in Elementary Mathematics Education program within a public university in Türkiye during the 2018–2019 academic year. The research concluded that PEMTs who learned linear algebra through MRBI and PBI approaches outperformed those who learned it through formalism-based methods. Furthermore, the two teaching approaches used in the experimental groups (PBI and MRBI) were effective in enhancing self-efficacy and in differentiating PEMTs’ levels of understanding demonstrated by students. In contrast, traditional teaching methods based on formalism did not lead to any significant changes in these areas.